Etude asymptotique des enlacements du mouvement Brownien autour des droites de l'espace
type: Item
instance of: scholarly article
title: Etude asymptotique des enlacements du mouvement Brownien autour des droites de l'espace
zbMATH Open document ID: 0594.60083
DOI: 10.1007/BF00363519
publication date: 1987-01-01T00:00:00Z
review text: The existence of a joint asymptotic distribution for the windings of a three-dimensional Brownian motion around a finite number of straight lines is obtained. This complements the recent studies by \textit{J. W. Pitman} and the second author [see, e.g. ''Asymptotic laws of planar Brownian motion.'' Ann. Probab. 14, 733-779 (1986)] and the authors [see e.g. Probab. Theory Relat. Fields 71, 183-229 (1986; Zbl 0579.60077)], of the joint asymptotic distribution for the windings of planar Brownian motion around a finite number of points. The following principle governs the passage from results in the plane to results in space: Let B be a three dimensional Brownian motion, and \(P_ 1,...,P_ k\), k planes which intersect two by two. Then, the convergence in distribution concerning the planar Brownian motion \(B^ i\) (1\(\leq i\leq k)\), defined respectively as the orthogonal projections of B on \(P_ i\) (1\(\leq i\leq k)\) take place jointly, and the corresponding limit variables are independent.
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 3956161
zbMATH Keywords: asymptotic distribution for the windings of a three-dimensional Brownian motion
author: J.-F. Le Gall
author: Marc Yor
MaRDI profile type: Publication
cites work: Q3911816
cites work: Q4153429
cites work: Étude asymptotique de certains mouvements browniens complexes avec drift
cites work: Q3717957
cites work: On D. Williams' “Pinching Method” and Some Applications
cites work: Asymptotic laws of planar Brownian motion
cites work: Some Theorems Concerning 2-Dimensional Brownian Motion
cites work: Q4727959
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Recommended article: Étude asymptotique de certains mouvements browniens complexes avec drift
Recommended article: Q5844284
Recommended article: Q4022486
Recommended article: Comportement asymptotique du mouvement brownien sur une variété homogène à courbure négative ou nulle. (Asymptotic behaviour of Brownian manifolds with non positive curvature)
Recommended article: Q3706285
Recommended article: Le mouvement brownien sur \({\mathbb{R}}^ N\), en tant que semi-martingale dans \(S_ N\)
Recommended article: Q5285459
Recommended article: Asymptotic behaviour of a Brownian motion on exterior domains
Recommended article: Q3357230
description: scientific article; zbMATH DE number 3956161